Light and the Theory of a Quasi-labile Ether. 137 



case is that ¥ and are not self-conjugate.* This is what we 

 might expect on the electric theory from the experiments of 

 Dr. Hall, which show that the operators expressing the relation 

 between electro-motive force and current are not in general 

 self-conjugate in this case. 



In the preceding comparison, we have considered only the 

 limiting cases of the two theories. With respect to the sense 

 in which the limiting case is admissible, the two theories do 

 not stand on quite the same footing. In the electric theory, or 

 in any in which the velocity of the missing wave is very great, 

 if we are satisfied that the compressibility is so small as to pro- 

 duce no appreciable results, we may set it equal . to zero in our 

 mathematical theory, even if we do not regard this as express- 

 ing the actual facts with absolute accuracy. But the case is 

 not so simple with an elastic theory in which the forces resist- 

 ing certain kinds of motion vanish, so far, at least, as they are 

 proportional to the strains. The first requisite for any sort of 

 optical theory is that the forces shall be proportional to the 

 displacements. This is easily obtained in general by supposing 

 the displacements very small. But if the resistance to one 

 kind of distortion vanishes, there will be a tendency for this 

 kind of distortion to appear at some places in an exaggerated 

 form, and even to an infinite degree, however small the dis- 

 placements may be in other parts of the field. In the case be- 

 fore us, if we suppose the velocity of the missing wave to be 

 absolutely zero, there will be infinite condensations and rare- 

 factions at a surface where ordinary waves are reflected. That 

 is, a certain volume of ether will be condensed to a surface, 

 and vice versa. This prevents any treatment of the extreme 

 case, which is at once simple and satisfactory. The difficulty 

 has been noticed by Sir William Thomson, who observes that 

 it may be avoided if we suppose the displacements infinitely 

 small in comparison with the wave-length of the wave of com- 

 pression. This implies a finite velocity for that wave. A similar 

 difficulty would probably be found to exist (in the extreme 

 case) with regard to the deformation of the ether by the mole- 

 cules of ponderable matter, as the ether oscillates among them. 

 If the statical resistance to irrotational motions is zero, it is not 

 at all evident that the statical forces evoked by the disturbance 

 caused by the molecules would be proportional to the motions. 

 But this difficulty would be obviated by the same hypothesis 

 as the first. 



These circumstances render the elastic theory somewhat less 



convenient as a working hypothesis than the electric. They 



do not necessarily involve any complication of the equations 



of optics. For it may still be possible that this velocity of the 



* See this Journal, vol. xxv, p. 113. 



